Benjamin Netanyahu will keep his job but head a much-weakened coalition government as the hawkish Israeli prime minister secured the support of a small conservative partner just minutes before the right to try to form a government was to be handed over to the opposition.

Mr. Netanyahu’s Likud Party will head a new government with just a bare-minimum 61-seat majority in the 120-seat Knesset, a sharp comedown from the big victory Mr. Netanyahu thought he had achieved by winning a clear plurality over the center-left Zionist Union in the general election seven weeks ago. His projected coalition of 67 seats in the Knesset has been reduced as potential allies shunned his government, and the prime minister was forced to grant a series of concessions to get smaller parties to sign on.

Analysts said the unexpectedly difficult horse-trading has cut into the prime minister’s clout on domestic issues and may complicate his efforts to head off the nuclear deal with Iran that President Obama hopes to complete by June.

The Israeli prime minister dissolved the previous government in December in the hopes of increasing his parliamentary majority. The slim hold on power of the new coalition raises the real possibility that Israelis will face another general election sooner rather than later.

“The coalition is getting off to a very rocky start,” said Natan Sachs, fellow at the Brookings Institution’s Center for Middle East Policy. “Netanyahu hoped for a far more stable coalition and one that did not depend on every individual member of the Jewish Home or other parties. With a razor-thin majority of one, he is beholden to every member of his coalition.”

The announcement of a new government came after Orthodox-Nationalist Jewish Home leader Naftali Bennett held out against a last-minute offer to join Likud’s coalition, which involved Cabinet positions in the ministries of education, diaspora, agriculture and culture and sports. Israeli press reports said that Mr. Bennett was pressing Mr. Netanyahu to secure the ministry of justice for a member of his party as well.

Mr. Bennett’s party strongly supports Israel’s settler community and opposes an independent Palestinian state, which could also complicate Mr. Netanyahu’s efforts to repair relations with Washington and with a number of European countries.

Reports Wednesday afternoon confirmed that Likud had acquiesced to Mr. Bennett’s demands, which one Likud official likened to “extortion,” according to Haaretz. “Bennett extorted us, and in this case, it seems his extortion will work for him,” the Likud official told the newspaper. “But extortion comes at a price, and Bennett will have to pay dearly in the future.”

Short-lived coalition?

The chances that the new coalition will last its full four-year term are slim, as no Israeli government has done so in over 30 years. The last Knesset only lasted two years before falling apart. Gil Hoffman, political analyst for the Jerusalem Post, said that despite being given a mandate until 2019, “no one thinks [the new government] will last that long.”

Mr. Hoffman added that the new Knesset “will be subject to tremendous international pressure … and that can make it harder to keep the government stable, especially when there are world leaders who don’t like Netanyahu personally.”

The coalition consists of Likud and four smaller conservative parties.

Mr. Netanyahu had until Wednesday to secure a coalition of a majority of the body’s 120 seats, according to Knesset election rules. If Netanyahu had failed, President Reuven Rivlin would likely have gone to runner-up Isaac Herzog, leader of the center-left Zionist Union party, to see if he could form a government.

Despite polls predicting a close race, Mr. Herzog’s party came in a distant second to Likud for the Knesset plurality last month, winning 24 seats to Likud’s 30. Immediately following the election, he announced that he would “challenge” the re-elected prime minister’s “extreme right-wing government.”

The vote also came shortly after Mr. Netanyahu’s controversial trip to Washington to address the Iran nuclear talks before a joint session of Congress, a trip in which President Obama refused to meet with the Israeli leader.

Mr. Netanyahu is expected to take over the foreign minister position, with the hope of later offering it to Mr. Herzog as a token of cooperation and potential fence-mending.

Mr. Netanyahu’s quest for a majority nearly foundered this week after Avigdor Lieberman, head of the secular nationalist Yisrael Beytenu party, unexpectedly announced that he would sit in opposition to a Likud-led coalition, calling the new government “opportunistic” and not “nationalistic.” Mr. Lieberman, who also said he would resign as Israeli foreign minister, said his party had “chosen our principles over Cabinet seats.”

The solidly conservative lineup of Mr. Netanyahu’s new coalition left some liberal factions and their U.S. supporters worried about the fallout for Israel’s international standing.

“This government, based on the ideology of its members, is bound to act to further hinder the viability of a two-state solution, to further exacerbate Israel’s isolation internationally, to intensify West Bank settlement construction, promote undemocratic legislation and act to stifle dissent,” said Debra DeLee, president and CEO of D.C.-based Americans for Peace Now.